1. Show that
   1. $\lg(n!)= \Theta(n\lg n)$
   2. $(\lg n)^{\lg n}=o(e^n)$
   3. $(\lg n)^2=o(\sqrt{n})$
2. Determine whether $5^{\lg n}=o(n^{5/2})$ or $n^{5/2}=o(5^{\lg n})$.

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